First, the research object of the history of mathematics
The history of mathematics is a science that studies the occurrence, development and laws of mathematical science, which is simply to study the history of mathematics. It not only traces the evolution and development process of mathematics contents, ideas and methods, but also explores various factors affecting this process and the influence of the development of mathematics science on human civilization in history. Therefore, the research object of the history of mathematics not only includes specific mathematical contents, but also involves social sciences and humanities such as history, philosophy, culturology and religion, which is an interdisciplinary subject.
In terms of research materials, archaeological materials, historical archives, historical mathematics original documents, various historical documents, ethnological materials, cultural history materials, interviews with mathematicians, etc. are all important research objects, among which mathematical original documents are the most commonly used and important first-hand research materials. From the research goal, we can study the evolutionary history of mathematical thoughts, methods, theories and concepts; We can study the interactive relationship between mathematical science and human society; You can study the history of the exchange and dissemination of mathematical ideas; You can study the life of mathematicians and so on.
The task of studying the history of mathematics is to find out the basic historical facts in the development of mathematics, reproduce its original features, and make scientific and reasonable explanations, explanations and evaluations on mathematical achievements, theoretical systems and development models through these historical phenomena, so as to explore the laws and cultural essence of the development of mathematical science. As the basic methods and means to study the history of mathematics, there are often historical textual research, mathematical analysis, comparative research and other methods.
Historians' duty is to tell history according to historical materials, and seeking truth from facts is the basic principle of historiography. Textual research has been formed in western history since17th century. It appeared earlier in China, especially in the Ganjia period of the Qing Dynasty, and it is still the main method of historical research. However, with the progress of the times, textual research methods are constantly improving and its application scope is expanding. Of course, it is necessary to realize that the historical materials are true or false, and the psychological state of the researchers involved in the research process will inevitably affect the choice of research materials and the results of the research. In other words, the authenticity of the conclusions of historical textual research is relative. At the same time, we should realize that textual research is not the ultimate goal of historical research, and the study of mathematical history cannot be textual research for textual research's sake.
If you can't compare, you can't think. All scientific thinking and investigation are inseparable from comparison, or comparison is the beginning of understanding. The development of today's world is multipolar, and different countries, regions and nationalities develop together in cultural exchanges. Therefore, with the development of the research on the history of multi-world civilization and the weakening of western centralism, heterogeneous regional civilization has been paid more and more attention, and the comparison of mathematical cultures in different regions and the research on the history of mathematical communication have become increasingly active. The comparative study of the history of mathematics often revolves around three aspects: mathematical achievements, mathematical scientific paradigm and the social background of mathematical development.
The history of mathematics belongs to both the field of historiography and the field of mathematical science. Therefore, the study of the history of mathematics should follow the laws of both history and mathematics science. According to this feature, mathematical analysis can be used as a special auxiliary means in the study of mathematical history. In the absence or lack of historical data, we can analyze the contents and methods of ancient mathematics from the height of modern mathematics, so as to trace the source, summarize the theory and put forward historical hypothesis. Mathematical analysis is actually a connection between "ancient" and "present".
Second, the stage of the history of mathematics
The development of mathematics has stages, so researchers divide the history of mathematics into several periods according to certain principles. At present, the academic community usually divides the development of mathematics into the following five periods:
1. The embryonic period of mathematics (before 600 BC);
2. The period of elementary mathematics (from 600 BC to1mid-7th century);
3. The period of variable mathematics (1mid-7th century to11920s);
4. Modern Mathematics Period (65438+11920s to World War II);
5. The period of modern mathematics (from the 1940s).
Third, the significance of the history of mathematics
(1) The scientific significance of the history of mathematics
Every science has its history of development. As a historical science, it is both historic and realistic. Its reality is first manifested in the continuity of scientific concepts and methods. Today's scientific research is to some extent the deepening and development of scientific tradition in history, or the solution of scientific problems in history, so we can't separate the relationship between scientific reality and scientific history. Mathematical science has a long history. Compared with natural science, mathematics is an accumulative science, and its concepts and methods are more continuous. For example, the decimal notation and the four arithmetic rules formed in ancient civilization have been used to this day. Historical issues such as Fermat's conjecture and Goldbach's conjecture have long been hot topics in the field of modern number theory, and materials of mathematical tradition and history can be developed in practical mathematical research. Many famous mathematicians at home and abroad have profound cultivation or research on the history of mathematics, and are good at drawing nutrients from historical materials, making the past serve the present and bringing forth the new. Wu Wenjun, a famous mathematician in China, made outstanding achievements in the field of topology research in his early years. In the 1970s, he began to study the history of Chinese mathematics, which opened up a new situation in the research theory and method of the history of Chinese mathematics. Especially inspired by China's traditional thoughts of mathematical mechanization, he established a mathematical mechanization method for mechanical proof of geometric theorems, which was called "Wu Fa" in history. His works are worthy of being a model of making the past serve the present and revitalizing national culture.
The reality of the history of science also lies in providing experience and lessons for our scientific research today, making us clear the direction of scientific research, avoiding detours or mistakes, providing a basis for today's scientific and technological development decisions, and also providing a basis for us to foresee the future of science. If we know more about the history of mathematics, we won't have such absurd things as drawing the third part of the solution angle and proving the four-color theorem, and we will also avoid wasting our time and energy on Fermat's last theorem and other issues. At the same time, summing up the experience and lessons in the history of mathematics development in China is beneficial to the development of mathematics in China today.
(2) the cultural significance of the history of mathematics
M Klein, an American mathematical historian, once said: "The general characteristics of an era are closely related to the mathematical activities of this era to a great extent. This relationship is particularly evident in our time. " Mathematics is not only a method, an art or a language, but also a rich knowledge system, which is very useful to natural scientists, social scientists, philosophers, logicians and artists and influences the theories of politicians and theologians. Mathematics has widely influenced human life and thought, and is the main force to form modern culture. Therefore, the history of mathematics reflects the history of human culture from one side and is the most important part of the history of human civilization. Many historians understand the characteristics and value orientation of other major ancient cultures through the mirror of mathematics. Mathematicians in ancient Greece (600 BC-300 BC) emphasized strict reasoning and the conclusions drawn from it, so they did not care about the practicality of these achievements, but educated people to make abstract reasoning and inspired people to pursue ideals and beauty. Through the investigation of the history of mathematics in Greece, it is very easy to understand why ancient Greece had beautiful literature, extremely rational philosophy and idealized architecture and sculpture that could not be surpassed by later generations. The history of Roman mathematics tells us that Roman culture is foreign, and the Romans lack originality and pay attention to practicality.
(3) the educational significance of the history of mathematics
When we have studied the history of mathematics, we will naturally feel that the development of mathematics is illogical, or that the actual situation of mathematics development is very inconsistent with the mathematics textbooks we have learned today. The mathematics content we learn in middle schools today basically belongs to the elementary mathematics knowledge before calculus in17th century, while most of the contents in the department of mathematics in universities are advanced mathematics in17th and18th century. These mathematics textbooks have been repeatedly tested and compiled under the guidance of the principle of combining science with educational requirements. They are knowledge systems that compile historical mathematical data according to certain logical structure and learning requirements, and inevitably abandon the actual background, knowledge background, evolution process and various factors that lead to the evolution of many mathematical concepts and methods. Therefore, it is difficult to obtain the original appearance and panorama of mathematics only by studying mathematics textbooks. At the same time, it ignores those mathematical materials and methods that have been eliminated by history but may be useful to real science, and the best way to make up for this deficiency is through the study of mathematical history.
In the eyes of ordinary people, mathematics is a boring subject, so many people regard it as a daunting task. To some extent, this is because our math textbooks often teach some rigid and unchangeable math content. If the history of mathematics is infiltrated into mathematics teaching to make mathematics alive, it will stimulate students' interest in learning and help deepen their understanding and understanding of mathematical concepts, methods and principles.
The history of science is an interdisciplinary subject of arts and sciences. Judging from today's educational situation, the gap between arts and sciences leads to the fact that the talents trained by our education are increasingly unable to adapt to today's modern society with high penetration of natural science and social science. It is precisely because of the interdisciplinary nature of the history of science that it can show the role of communicating arts and sciences. Through the study of the history of mathematics, students in the department of mathematics can receive the training of mathematics major and get the cultivation of humanistic quality, while students in liberal arts or other majors can learn the general situation of mathematics and get the cultivation of mathematics and physics through the study of the history of mathematics. The achievements and moral character of mathematicians in history will also play a very important role in the personality cultivation of teenagers.
Mathematics has a long history in China. /kloc-Before the 4th century, it was the most developed country in the world. Many outstanding mathematicians have appeared and made many brilliant achievements. Its long history, calculation-centered, programmed and mechanized algorithmic mathematical model and the axiomatic mathematical model characterized by geometric theorem deduction and reasoning in ancient Greece reflect each other and alternately influence the development of world mathematics. Due to various complicated reasons, China became a mathematical superpower after16th century. After a long and difficult development process, it gradually merged into the trend of modern mathematics. Due to educational mistakes, under the influence of modern mathematical civilization, we often forget our ancestors and know nothing about the traditional science of our motherland. The history of mathematics can help students understand the brilliant achievements of ancient mathematics in China, the reasons for the backwardness of modern mathematics in China, the present situation of modern mathematics research in China and the gap with developed countries, thus stimulating students' patriotic enthusiasm and revitalizing national science.